A three-step approach to reliably estimate magnetic field strengths in star-forming regions

Abstract

The magnetic field is known to play a crucial role in star formation. Dust polarization is an effective tool for probing the morphology of the field, yet it does not directly trace its strength. Several methods have been developed, combining polarization and spectroscopic data, to estimate the strength of the magnetic field, including the DCF method, which relates these quantities to the magnetic-field strength under the assumption of Alfv\'enic turbulence. Skalidis & Tassis (2021) (ST), relaxed this assumption to account for the compressible modes, deriving more accurate estimates of the field strength. We evaluate the accuracy of these methods in star-forming regions and propose a systematic approach for calculating the key observational parameters involved: the velocity dispersion (dv), the dispersion of polarization angles (d\theta), and the cloud density (rho). We use a 3D MHD chemodynamical simulation of a turbulent molecular cloud and generate synthetic observations, for seven different inclination angles. We employ various approaches for estimating the parameters dv, d\theta, and rho and find that the approach used to calculate these parameters plays a crucial role in estimating the magnetic field strength. We show that the value probed by both the DCF and ST methods corresponds to the median of the molecular-species-weighted POS component of the magnetic field. The ST outperforms DCF, accurately following the expected cosine trend with respect to the inclination angle, and remains within 1\sigma from the true strength of the field. Based on our analysis, we proposed that, in self-gravitating clouds, the intrinsic parameters (rho, dv, d\theta) should be calculated as follows: rho using radiative transfer analysis, dv using the second moment maps, and d\theta by fitting Gaussians to the polarization angle distributions to remove the contribution of the hourglass morphology.